New Irreducible Modules for Heisenberg and Affine Lie Algebras

Details New Irreducible Modules for Heisenberg and Affine Lie Algebras New Irreducible Modules for Heisenberg and Affine Lie Algebras

2011-07-05

arxiv.org/abs/1107.0893v1

Mathematics

Representation Theory

17 pages

Scientific paper

We study $\mathbb Z$-graded modules of nonzero level with arbitrary weight multiplicities over Heisenberg Lie algebras and the associated generalized loop modules over affine Kac-Moody Lie algebras. We construct new families of such irreducible modules over Heisenberg Lie algebras. Our main result establishes the irreducibility of the corresponding generalized loop modules providing an explicit construction of many new examples of irreducible modules for affine Lie algebras. In particular, to any function $\phi:\mathbb N\rightarrow \{\pm\}$ we associate a $\phi$-highest weight module over the Heisenberg Lie algebra and a $\phi$-imaginary Verma module over the affine Lie algebra. We show that any $\phi$-imaginary Verma module of nonzero level is irreducible.

Affiliated with

Also associated with

No associations

Rating

New Irreducible Modules for Heisenberg and Affine Lie Algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with New Irreducible Modules for Heisenberg and Affine Lie Algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and New Irreducible Modules for Heisenberg and Affine Lie Algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-477465